Just to add on to petr k.'s answer, ArcGIS Engine has the capability to load an MXD into the MapControl and it can load layer files.

If you are loading the same DBF file each time you run the application, you can create an MXD using ArcMap to setup your symbology and then load the MXD into ArcGIS Engine at runtime.

Alternatively, you can configure layer symbology in ArcMap and then right click on it, hit Save to Layer. You can then load this layer into your MapControl using IMap::AddLayer or by opening it as an ILayerFile.